Question

The population of a town is increased by 15% in the first year and 8% in the second year, but decreased by \(12\frac{1}{2}\%\) in the third year. If the population at the end of the third year is 26,082, find the original population of town.
1. 30,000
2. 25,000
3. 24,000
4. 28,000

Answer 1

Correct Answer - Option 3 : 24,000

Given:

The increase in population first year = 15%

The increase in population second year = 8%

The decrease in population third year = 12 (1/2)%

The population at the end of the third year = 26,082,

Calculation:

Let the initial population be x.

The population at the end of first year = x × 115%

The population at the end of second year = (x × 115%) × 108%

The population at the end of third year = (x × 115%) × 108% × [100 - (25/2)]% = 26082

(x × 115%) × 108% × [100 - (25/2)]% = 26082

x × (115/100) × (108/100) × (175/200) = 26082

Simplifying and solving, 

x = 24,000

∴ The initial population is 24,000.